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Primes of the form n^7-n-1.
+10
3
2097143, 1801088519, 21869999969, 42618442943, 78364164059, 137231006639, 194754273839, 435817657169, 678223072799, 1174711139783, 1727094849479, 3938980639103, 4398046511039, 4902227890559, 6722988818363, 19203908986079
MAPLE
map(t -> t^7-t-1, select(t -> isprime(t^7-t-1), [$1..10^4])); # Robert Israel, Jul 22 2019
MATHEMATICA
k = 7; a = {}; Do[If[PrimeQ[x^k - x - 1], AppendTo[a, x^k - x - 1]], {x, 1, 100}]; a
Select[Table[n^7-n-1, {n, 80}], PrimeQ] (* Harvey P. Dale, Jun 20 2020 *)
CROSSREFS
Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426, A126427, A126427, A126428, A126429, A126430, A126431, A126432 A126433, A126434.
Primes of the form k^8-k-1.
+10
3
1679609, 5764793, 99999989, 4294967279, 282429536453, 377801998307, 5352009260441, 16815125390579, 39062499999949, 72301961339081, 83733937890569, 281474976710591, 513798374428571, 1113034787454899
MATHEMATICA
k = 8; a = {}; Do[If[PrimeQ[x^k - x - 1], AppendTo[a, x^k - x - 1]], {x, 1, 100}]; a
Select[Table[k^8-k-1, {k, 80}], PrimeQ] (* Harvey P. Dale, Nov 06 2021 *)
CROSSREFS
Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426, A126427, A126427, A126428, A126429, A126430, A126431, A126432 A126433, A126434, A126434.
Primes of the form n^9-n-1.
+10
2
509, 262139, 10077689, 387420479, 68719476719, 118587876479, 1207269217769, 7625597484959, 10578455953379, 129961739795039, 327381934393919, 1628413597910399, 1953124999999949, 5416169448144839, 10077695999999939
MATHEMATICA
k = 9; a = {}; Do[If[PrimeQ[x^k - x - 1], AppendTo[a, x^k - x - 1]], {x, 1, 100}]; a
Select[Table[n^9-n-1, {n, 100}], PrimeQ] (* Harvey P. Dale, Mar 09 2016 *)
CROSSREFS
Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426, A126427, A126427, A126428, A126429, A126430, A126431, A126432 A126433, A126434, A126435, A126436, A126437.
Least prime of the form x^n-x-1.
+10
1
5, 5, 13, 29, 61, 2097143, 1679609, 509, 1021, 8589934583, 4093, 67108859, 16381, 470184984569, 4294967291, 2218611106740436979, 68719476731, 1350851717672992079, 1048573, 10460353199, 4194301, 20013311644049280264138724244295359, 16777213, 108347059433883722041830239, 20282409603651670423947251285999, 58149737003040059690390159, 72057594037927931, 536870909, 999999999999999999999999999989
MATHEMATICA
a = {}; Do[k = 2; While[ ! PrimeQ[k^n -k - 1], k++ ]; AppendTo[a, k^n - k - 1], {n, 2, 30}]; a (*Artur Jasinski*)
CROSSREFS
Cf. A002327, A002328, A116581, A126420, A126421, A126422, A126423, A126424, A126425, A126426, A126427, A126427, A126428, A126429, A126430, A126431, A126432 A126433, A126434, A126435, A126436, A126437, A126438.
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